If it weren’t for the Middle East — the Cambridge club, not the region — NYC’s latest musical cause célèbre might not exist. Since they emerged in 2004 with a pair of ambitious, math-rocky instrumental EPs, Battles have been saddled with the dubious “supergroup” tag. Take this SF Weekly introduction: “Something of an indie supergroup, the New York quartet comprises Ian Williams (Don Caballero, Storm and Stress), Dave Konopka (Lynx), John Stanier (Tomahawk, Helmet), and multi-instrumentalist Tyondai Braxton (son of avant-garde jazz legend Anthony Braxton, and a composer in his own right).” Sure, Bay Area musos have probably at least heard of Don Caballero, Helmet, and Anthony Braxton. But who the hell are Lynx? What a quick Google search won’t tell you that a post-college-age local music fan might is that Lynx were part of the burgeoning post-rock scene of the late ’90s/early ’00s — see Helms, Victory at Sea, the Wicked Farleys, et al. It was at Don Cab/Lynx shows at the Middle East that Williams became friends with Konopka, a Worcester native who’d come to Boston to attend MassArt. And that planted the seeds for what became Battles.

Konopka says he has “nothing but fond memories” of the years he spent in Boston. “It was a really good scene going on back then — pretty tight camaraderie, which was nice,” he says from Battles’ Dodge Sprinter, which is on its way to Albuquerque from Amarillo, where the band spent a day off from their North American tour in support of their much ballyhoo’d full-length debut, Mirrored (Warp). The tour hits the Paradise this Wednesday.

Konopka goes on to cite the band’s uneasiness with the “supergroup” label as a primary reason they waited so long to release a full-length. “The initial idea behind the EPs was that we were developing as band, and we had a body of work that we wanted to get out, but we didn’t want to put out that music as a full-length because there was already this thing, like this label hanging over our heads saying that we were a supergroup . . . and we wanted to avoid a grand entrance.”

The EPs, which Warp re-released in early 2006 as EP C/B EP, were well received, and eagerness for a full-length grew. After an intense period of writing at a Brooklyn rehearsal space in Williamsburg — “All four of us were firing on all cylinders,” says Konopka of the process, which he describes as a “25 percent democracy” — the band headed to Pawtucket for an even more intense three months of recording at Machines with Magnets, a studio run by Konopka’s old friend Keith Souza. Along with Souza and two assistants, Battles holed up in the studio from the beginning of October to Christmas Eve of last year.

What they emerged with defies categorization. Mirrored marries the complexity and instrumental proficiency of math rock with the sounds, textures, and rhythms of electronic dance music, the forward-thinking audacity of prog with the sod-off spirit of punk rock. The seven-minute second track, “Atlas,” combines a schaffel beat — a sort of shuffle that became popular in European dance clubs a few years ago — with a mind-twisting, Pee-wee-era Danny Elfman melody and surreal vocals that have been manipulated so that Braxton sounds something like a Munchkin from The Wizard of Oz. But more important than any genre Frankensteining is the quality of the songs: the hooks are hummable, the beats are contagious, and the overall effect is thrillingly disorienting. The most common word that’s been applied to Battles’ music is “futuristic,” and if this is what the future sounds like, then maybe things won’t be so bad after all.

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